Systems and methods for determining the position of a tool in a borehole



Jan. 20,1197() SYSTEMS AND M Filed May 2, 196e W. A. WHITFILL, JR ETHODSFOR DETERMINING THE POSITION OF A TOOL IN A BOREHOLE 9 Sheets-Sheet 1 rVl Jam 20, 1970 W. A. WHITFILL, JR` 3,490,150

SYSTEMS AND METHODS FOR DETERMINING THE POSITION OF A TOOL IN A BOREHOLEI Filed May 2. 1966 9 Sheets--Sheetl 2 fg 10?. 2A

Jan- 20, 1970 w. A.wH|TF||.| JR 3,490,150 I .SYSTEMS AND METHODS FORDETERMINING THE POSITION 0F A T001.. IN A BOREHOLE Filed May 2, 1966 9Sheets-Sheet 3 Jam 20, 1970 w. A. WHITFILL. .1R 3,490,150

SYSTEMS AND' METHODS FOR DETERMINING THE POSITION OF A TOOL IN ABOREHOLE 9 Sheets-Sheet 4 Filed May 2, 1966 Jan. 20, 1970 Filed-May 2,1966 //3 1 y l /56 fou/v7.65 fe 1 f;

R L I i a5/c /50 J WIA. WHITFILL, JR SYSTEMS AND METHODS FOR DETERMININGTHE POSITION OF A TOOL IN A BOREHOLE QSheets-S'heet 5 Jan. 20, 1970 w.A. WHlTFlLl., .1R 3,490,150

SYSTEMS AND METHODS FOR DETERMINING THE POSITION OF A TOOL IN A BOREHOLEJan. 20, 1970 w. A. wHlTFlLL. .1R 3,490,150 SYSTEMS AND METHODS FORDETERMINING THE POSITION OF A TOOL IN A BOREHOLE Filed May 2, 196e 9Sheets-S'heet '7 Jan. 20, 1970- w. IA. WHITFILL, JR 3,490,150

SYSTEMS AND METHODS FOR DETERMINING THE POSITION OF A TOOL IN A BOREHOLEFiled May 2, 1966 9 Sheets-*Sheet 8 Jan, 20, 1970 W. A. WHITFILL, J'R3,490,150

SYSTEMS AND METHODS FOR DETERMINING T'HE POSITION OF A TOOL IN ABOREHOLE Filed May 2, 196e 9 sheets-sheet 9 C Tfr/56m u2) I i... y/H

(c) MAC/e c (f) ,uw fawn/Mn (mf J//ar Ma) United States Patent O U.S.Cl. 33-133 39 Claims ABSTRACT OF THE DISCLOSURE In accordance with anillustrative embodiment of the present invention, methods and apparatusare shown for continuously and accurately determining the position of acable supported tool in a borehole. To accomplish this, the movement ofthe cable at the surface of the earth and the tension in the cable atthe tool and at the surface of the earth are measured and combined inaccordance with a given relationship to produce a corrected cablemovement measurement. Additionally, a calibration correction functionand a correction function for cable stretch with temperature can beutilized for additional depth correction. The accumulation of thiscorrected cable movement measurement will then give the position of thetool in theborehole. If desired, this position can be referred to adepth position corresponding to drill pipe length.

This invention relates to systems and methods for accurately andcontinuously determining the length of an elastic cable under tension,and more particularly, to systems and methods for determining the trueposition of a tool or device suspended on the end of an elastic cable,as the tool or device on the end of the cable is moved up and down.

This invention is particularly adapted for use in the logging of anearth borehole where measurements of the surrounding subsurface earthformations are taken at different depths throughout the borehole bymeans of a measuring device which is lowered into the borehole at theend of a supporting cable extending from the surface of the earth.Typically, the measurements taken along the length of the borehole areintended to provide indications of oil or gas bearing strata. Therefore,the depth of the logging or measuring device below the surface of theearth must be accurately determined at all times so that themeasurements may be accurately correlated with the true depth of thelogging or measuring device.

To determine the depth of the logging or measuring device in theborehole, a means of determining the length of cable that is loweredinto the borehole may be utilized to count the actual number of feet ofcable lowered into the borehole by a cable reeling device located at thesurface of the earth. Many systems have been proposed for measuring thiscable length, and thus the position of the measuring or logging devicewithin the borehole. Some of these are sheave devices located at thesurface of the earth -which provide a measurement of the length of cablewhich passes over the sheave. Other systems utilize a sensing deviceresponsive to magnetic marks on the cable along the length of the cable,which systems measure the length between the magnetic marks as the cableis payed out or taken in.

However, there are forces at work on the measuring or logging devicewithin the borehole which sometimes cause these cable length indicatingdevices at the surface of the earth to give readings which do not havethe desired accuracy. Some of these forces include the weight of themeasuring or logging device and the weight of the cable Patented Jan.20, 1970 MDice which connects it to the cable reeling device at thesurface of the earth, the buoyant force of the drilling liquid or mud inthe borehole, and the drag or frictional forces applied by both thedrilling liquid or mud and by the wall of the borehole to both the cableand the measuring or logging device.

When investigating earth formations surrounding the borehole, themeasuring or logging device is generally lowered to the bottom of theborehole and the logging measurements are taken as the logging devicemoves up the borehole. However, when the cable reeling device at thesurface of the earth is stopped upon reaching the vicinity of the holebottom, the logging device at the end 0f the great length of cable willcontinue moving downward for some distance due to the forces acting onthe logging device and cable, and the elasticity of the cable. However,the depth indicator at the surface of the earth will stop at the momentthe cable reeling device is stopped. As a result, the depth indicatingdevice at the surface of the earth will give an erroneous depthindication of the logging tool at the bottom of the borehole.

In addition, when the cable reeling device begins reeling the cable in,thus moving the logging tool up the borehole, the forces acting on thelogging tool and the cable will cause the -cable to stretch, thuscausing the logging tool to be located at a different depth than thedepth indicated on the depth indicating device at the Surface of theearth. Also, when the cable reeling device changes speed, the loggingtool tends to change to a different depth than that indicated on thedepth indicating device.

These errors introduced by the stretching of the cable can be excessivefor the accurate determination of the depth of oil-bearing strata.Oil-bearing strata may be two or three feet or less in thickness in manycases. Since the error of the depth indicating system can in some casesbe several feet, the subsequent perforation operation performed duringthe well-completion stage may miss the oil-bearing strata.

Various systems for obtaining the average depth error of a loggingdevice on the end of an elastic cable in a borehole have been proposed.One proposed way in which an average measure of depth error is obtainedis by inserting magnetic marks on a cable which has a xed force on theend thereof, thus placing a fixed tension on the cable. These magneticmarks are inserted at delinite intervals along the length of the cableand counted as the cable is reeled in or out at the surface of theearth. The depth indicated by the magnetic marks are then combined witha cable tension measurement made at the surface of the earth to providea depth correction. Such a system is shown in U.S. Patent No. 3,067,519,granted to G. Swift on Dec. 11, 1962.

Another surface-located cable tension method for providing an averagecorrection of depth errors is shown in U.S. Patent No. 3,027,649 grantedto Raymond W. Sloan on Apr. 3, 1962.

However, there are serious errors which may occur when thesepreviously-proposed systems are utilized. For example, when the loggingdevice becomes momentarily stuck against the wall of the borehole as thedevice is moving through the borehole, the logging device will be at aconstant depth, while at the same time the depth indicator at thesurface of the earth 'is continually moving, thus introducing anexcessive error into the indicated depth. On the other hand, when thelogging device becomes unstuck, the elasticity of the cable will causethe logging device to move at a great rate beyond the depth indicated-by the depth measuring device at the surface of the earth, and willfrequently oscillate before reaching equilibrium.

The previously-proposed depth measuring systems can only provide anaverage measure of the depth changes encountered by the logging devicein the borehole because they utilize only measurements made at thesurface of the earth and because thousands of feet of cable usuallyseparate the downhole logging device and the surface-located cablemeasuring devices. For example, a force applied at the logging device inthe borehole would not appear immedi-ately at the surface of the earthin the form of a change in tension because of the great length of cable,and the measured force appearing at the surface of the earth in the formof a tension measurement would be distorted because of damping by thecable. These tension variations occurring at the logging device withinthe borehole may be delayed by as much as several seconds from reachingthe surface of the earth due to this travel time in the cable.

Thus, it can be seen that a device located at the surface of the earthfor measuring depth error by the method of transferring the force fromthe logging device within the borehole through the cable to the surfaceof the earth, does not give an instantaneous indication of the truedepth location of the logging device within the borehole. At best, itcan only give an average type indication.

Aside from instantaneous indications of depth, when only a surfacetension measurement is utilized, the tension existing at the bottom ofthe cable in the borehole can only be assumed to be constant at aparticular predetermined reference tension which has been chosen beforea logging run into the borehole. But, as a matter of fact, the tensionexisting on the lbottom portion of the cable does not necessarily remainat the predetermined reference tension due to, among other things, thecable and tool dragging against the side of the borehole.

Other problems niay also be encountered when using a surface depthmeasuring system. When the ear-th strata surrounding the borehole areinvestigated, the location and quantity of oil cannot always bedetermined by any one investigating method. In many cases, severaldifferent investigating methods have to be utilized and the dataobtained therefrom combined and analyzed before an oilbearing strata canbe located. Existing apparatus for carrying out these differentinvestigating methods sometimes cannot all be lowered into the boreholeat the same time. Thus, the various logging tools must sometimes belowered into the borehole at different times and on different loggingruns. To combine all of the various logging readings made -by thedifferent investigating tools in such a manner as to determine the exactlocation of oil-bear ing strata, the depth indications of each loggingrun must correlate very accurately with one another or else thecombination, analysis, and computation of the different measurementstaken with different measuring or logging tools will not provide thedesired result. To combine these various logging runs in such a way thatthe computations taken therefrom will provide the desired information,the depth indications from the various logging runs must be accurate towithin approximately several inches or less of one another.

One present-day example of multiple logging runs in the same boreholeconcerns the automatic computation of the apparent resistivity Rwa ofthe naturally occurring water within the porous formations surroundingthe borehole. To obtain Rwa, a previously-recorded induction log run isplayed back in depth synchronism with a sonic log being presently run.The sonic and induction log data are continuously fed to a computer tocalculate the value of Rwa, and the computed RWa is simultaneouslyrecorded with the sonic log. It can be seen that the depth of the sonicand induction logs must be accurate with respect to one `another toobtain an accurate calculation of Rw.

It is also desirable to have an accurate indication of 'the velocity ofthe measuring or logging tool moving through the borehole. For example,when a dipmeter is run through the borehole to determine the dip of theadjacent earth strata, that is, the angle that the bedding plane 'of theearth strata differs from the horizontal, the distance M beWeen signalindications on different circumferential points around the borehole isobtained by moving the dipmeter across a boundary between differentearth strata having different resistivity characteristics. This distanceM is given by the formula:

where M is the actual distance between the indications, Mr is theindicated distance between the indications, V, is the indicated velocityof a recorder located at the surface of the earth, and Vd is the averagevelocity of the dipmeter tool over the interval between the indications.It can be seen that if the actual velocity of the dipmeter is differentfrom the recorder velocity, the error in M will be given by the formula:

M -M Vd -Vt Mr Vr Thus, when the actual velocity of a dipmeter tool isdifferent from the recorder velocity, an error in the computed dip ofthe earth bed will occur. If, however, the actual instantaneous deptherror is corrected, the velocity error will also be automaticallycorrected.

When determining the depth of the logging tool within the borehole, itis desired to have the device at the surface of the earth which measuresthe length of cable reeled in or out, to provide indications of thelength of cable at very short intervals, as for example, one-quarterinch, so that the depth correction can be made at shorter intervals.However, if there is a very small error present at each onequarter inchindication from the surface cable length measuring device, it willaccumulate to a substantial depth error when multiplied by thousands offeet. Such a small error could arise from manufacturing tolerances inthe device. Thus, it would be desirable to provide a means toperiodically correct for any depth error caused by the cable lengthmeasuring device at the surface of the earth.

It has been found that the elongation of the cable also depends upon thetemperature within the borehole. This borehole temperature increases asthe depth in the borehole increases. Thus, it would be desirable toprovide a means to correct for cable stretch due to the boreholetemperature as the logging tool is raised or lowered in the borehole.

Additionally, the borehole depth is usually referred to the total depthas determined by the lengths of drill pipe used to drill the hole, thelength of each drill pipe being measured at the surface of the earthwithout pressure or temperature forces acting on it. Thus, this drillpipe determined total depth will not correlate accurately with the truedepth within the borehole. Since the drill pipe depth frequently is thedepth utilized in perforating oil-bearing strata, the actual true depthmust be referred to the drill pipe depth. The difference between drillpipe depth and the true or actual depth will increase as the depth ofthe borehole increases. Thus, it is desirable to provide a means tocorrect for this drill pipe depth error as the depth of the boreholeincreases and refer the true or actual depth to the drill pipe depth.

It can be seen from the foregoing that many factors should be taken intoconsideration in order to arrive at a highly accurate indication ofborehole depth. The actual length of cable passing over a given point atthe surface of the earth should be combined with a function representingthe tension on the cable at the surface of the earth and a functionrepresenting downhole tension to obtain both the average and theinstantaneous value of depth caused by changes in tension. These factorsshould be combined with a function representing correction of the lengthmeasuring device at the surface of the earth caused from inaccuratemanufacturing tolerances, a function representing the changes in lengthof the logging cable due to downhole temperature, and a functionrepresenting a correction due to referring the actual true depth to thedrill pipe depth. It would entail a great amount of diiculty andinaccurateness to provide separate means for each and every one of theabove corrections. It would therefore be desirable to provide one devicefor continuously and automatically correcting for all of theabovementioned sources of depth error and to provide one output to drivea recorder in accordance with the desired value of depth.

It is an object of the invention therefore, to provide new and improvedmethods and apparatus for determining the true depth of a device in aborehole. E

It is another object of the invention to provide new and improvedmethods and apparatus for correcting the depth error caused by theaverage stretch of a cable used in a borehole.

It is still another object of the invention to provide new and improvedmethods and apparatus for correcting the depth error caused byinstantaneous changes of force acting on a cable and tool within aborehole.

It is still another object of the invention to provide new and improvedmethods and apparatus for correcting for the stretch of a cable causedby temperature variations within the borehole.

It is still another object of the invention to provide new and improvedmethods and apparatus for correcting for depth errors caused byerroneous cable length indications from a device at the surface of theearth, which device determines the length of a cable reeled in or out atthe surface of the earth.

It is still another object of the invention to provide new and improvedmethods and apparatus for referring true depth measurements to drillpipe depth measurements.

It is still another object of the invention to provide new and improvedmethods and apparatus for correcting the depth indication provided by acable-measuring device that determines the length of cable being reeledin or out at the surface of the earth wherein such depth correction isobtained from the tension on the cable at the surface of the earth, thetension 0n the cable at the downhole end thereof, a calibrationcorrection for the cable-measuring device, the depth error caused bystretch of the cable due to temperature variations within the borehole,and a correction obtained from referring the true depth to the drillpipe depth.

It is still another object of the invention to provide new and improvedmethods and apparatus for automatically and continuously providinghighly accurate borehole depth indications.

In accordance with one feature of the invention, a system fordetermining the position or changes in position of a tool in a boreholecomprises rst means for generating a series of pulses representative ofthe length or amount of movement of cable payed out and taken in at the-surface as the tool is lowered and raised in the borehole and secondmeans for generating a first signal representative of a cable lengthcharacteristic, said characteristic causing said cable length ormovement indicated by said first means to be different from the desiredcable length or movement indication. The system further comprises meansfor generating a second signal derived from said first signal and saidseries of pulses and representative of the desired cable length ormovement indication, said third means including means for inhibitingselected ones of said pulses or adding new pulses to said series ofpulses from said first means to produce a corrected series of pulsesrepresentative of tool movement.

In accordance with another feature of the invention a method ofdetermining the position or changes in position in a borehole of a toolcomprises generating a series of pulses representative of the length oramount of movement of cable payed out and taken in at the surface as thetool is lowered and raised in the borehole and generating a first signalrepresentative of a cable length changing characteristic. The methodfurther comprises deriving a cor'- rection signal indicative of acorrection to be made to said series of pulses in response to the rstsignal and correcting the series of pulses by inhibiting selected onesof said pulses or adding new pulses to said series of pulses in responseto the correction signal. The method also includes generating an outputrepresentative of the desired depth or movement indication of said toolin response to the corrected series of pulses. It will be appreciatedthat since the tool is located at the end of the cable, cable length andtool position are synonymous and can be used interchangeably throughoutthe specification and claims.

IFor a better understanding of the present invention, together withother and further objects thereof, reference is had to the followingdescription taken in connection with the accompanying drawings, thescope of the invention being pointed out in the appended claims.

Referring to the drawings:

FIG. 1 is a schematic illustration showing one embodiment of the presentinvention;

FIG. 2 is a more detailed schematic diagram of portions of the FIG. lapparatus and is divided into FIGS. 2(a)and 2(b);

FIG. 3 is a schematic diagram showing portions of the FIG. 1 and FIG. 2apparatus in still greater detail and is divided into FIGS. 3(a), 3(b)and 3(c);

FIG. 4 is a circuit diagram of an analog computer circuit which may beutilized with the present invention;

FIG. 5 is a graph showing the stretch of a cable versus the depth of alogging tool within the borehole under typical borehole conditions;

FIGS. 6(a) and 6(b) are log-log graphs showing the frequency response ofcertain filters to be utilized with the present invention;

FIGS. 7(a)-7(h) are timing diagrams illustrating electrical pulses atvarious points within the FIGS. 1-3 apparatus; and

FIG. 8 represents how FIGS. 2(a) and 2(1)) and FIGS. 3(a), 3(b) and 3(c)are to be positioned to obtain single representations of FIGS. 2 and 3.

Referring to FIG. l of the drawings, there is shown a representativeembodiment of apparatus constructed in accordance with the presentinvention for continuously and automatically providing correctedindications of depth of a logging device 10 lowered in a borehole 11filled with a drilling mud 11a for investigation of the earth formationssurrounding the borehole 11. The logging tool 10 is a three electrodefocused electrical logging system wherein a survey current is emittedfrom a central survey electrode A0 and is confined to a pathhorizontally outward from the borehole 11 by focusing currents emittedfrom focusing electrodes A1 located above and below electrode A0. Thus,the portion of the surrounding earth formations that are investigatedare those portions adjacent to central survey electrode A0. It can beseen that only a small vertical portion of the surrounding earthformation is investigated at any one time and thus, the depth of centralsurvey electrode A0 must be accurately known before any oil-bearingearth strata indicated by the logging tool can be accurately penetrated.The three electrode focused system 10 shown in FIG. 1 is only anillustrative example and any type of logging tool could be utilized inplace thereof.

During a typical logging run, measurement signals are supplied to arecorder 14 by way of conductors 15 and 16 running through armoredmulti-conductor cable 12 to electrical measurement circuitry containedwithin a housing unit 10a within the logging tool 10. If, now, thelogging tool 10 were withdrawn from the borehole 11 after a rst loggingrun and another logging run made with another type of logging tool, asfor example, a sonic or induction logging tool, the sonic or inductionlog should be recorded in depth synchronism with the previously run log.The depths on the two logs must coincide exactly in order for theinformation obtained from both of the logs to be combined by a computerand provide accurate computations.

As the cable 12 is reeled in and out of the borehole 11 over anidler-pulley 17 by means of a suitable drum and winch mechanism (notshown) located at the surface of the earth, a length indicating wheel 18rotates with the movement of cable 12. Thus, the rotation of wheel 18 isproportional to the length of cable 12 that moves past wheel 18. Wheel18 is connected to a length measuring device 19 which provides depthindications to a depth correction computer 20. The idler-pulley 17 ismechan-v ically connected to a rigid member 21 by a tension measuringdevice 22 such that the full force exerted on idler-pulley 17 by cable12 and tool 10 is exerted on tension measuring device 22. Tensionmeasuring device 22 is electrically connected to a bridge circuit 23,whose electrical output is connected to an input of a low-pass filter55. The electrical output of low-pass filter 55 is connected to an inputof a multiple-input of depth correction computer 20. A calibrationcorrection means 24 and a stretch coeicient input means 25 are connectedto ad ditional inputs of depth correction computer 20.

Connected to a further input of depth correction computer 20 is a drillpipe correction means 26. The voltage on the wiper arm of apotentiometed 28 provides the output from drill pipe correction means 26to depth correction computer 20. The resistance portion 29 ofpotentiometer 28, which wiper arm 27 contacts, has a plurality ofvariable resistors 30 connected in parallel across segments of theresistance portion 29 of potentiometer 28. Connected across the ends ofthe resistance portion 29 of potentiometer 28 is a battery 31, thepositive terminal of which is connected to ground.

Connected to another input of depth correction cornputer 20 is atemperature correction means 32. The output to depth correction computer20 from temperature correction means 32 is supplied from the wiper arm33 of potentiometer 34. The resistance portion 35 of p0- tentiometer 34has a plurality of variable resistances 36 connected across segments ofresistance portion 35. Connected across the ends of resistance portion35 of potentiometer 34 is a battery 37, the negative terminal of whichis connected to ground.

Looking now at the downhole tension portion of the FIG. 1 apparatus,there is shown a downhole tension i device 38 connected between thelogging device 10 and the cable 12. Tension device 38 has twosemi-conductor strain gage elements, R2 and R4 which vary in resistanceas the tension between cable 12 and tool 10 varies. Strain gage elementsR2 and R4, which are preferably of the semi-conductor typeSPB3-12-100C6, manufactured by Baldwin-Lime-Hamilton are connected tothe bridge circuit 39, which comprises resistors R1 and R3 along withthe semi-conductor strain gage elements R2 and R4. The semi-conductorstrain gage elements R2 and R4 are represented in bridge circuit 39 bythe dotted line resistances R2' and R4'. The resistors R1 and R3 arealso preferable of the semi-conductor type, used for temperaturecompensation.

A DC power supply 40 located at the surface of the earth supplies DCpower via a conductor 43 to an oscillator 40 and an amplifier 41 locatedwithin the downhole housing unit a. `Conductor 43 is actually containedwithin cable 12 but, for simplicity, is shown separately. A pair ofinductors 43a and 43h, inductor 43a being connected between DC powersupply 40 and conductor 43 and inductor 43b being connected between theDC power inputs to amplifier 41 and oscillator 40 and conductor 43, areutilized to isolate the DC and AC loads. One output of oscillator 40 isconnected to the junction between resistor R1 and semi-conductor straingage element R4 of bridge circuit 39. The other output of oscillator 40is connected to the junction between resistor R3 and semiconductorstrain gage element R2. One input to amplifier 41 from bridge circuit 39is connected to the junction between resistor R1 and semi-conductorstrain gage element R2. The other input to amplifier 41 is connected tothe junction between resistor R3 and semi-conductor strain gage elementR4. The Aoutput from amplifier 41 is connected through a capacitor 42 toconductor 43. At the surface of the earth, a capacitor 44 is connectedbetween conductor 43 and amplifier 45. One output of amplifier 45 isconnected to a phase-sensitive detector 46. The other output fromamplifier 45 is connected to a voltage-limit ing circuit 47, the outputof which is connected to phasesensitive detector 46 to provide aphase-reference signal thereto. The output of phase-sensitive detector46 is connected to the input of an analog computer 48 to which also issupplied a function indicative of the damping coefficient B from dampingcoeicient input means 57, which function is constant for a givenborehole but varies from borehole to borehole. Also supplied to analogcornputer 48 is a function indicative of the cable stretch coefficient Efrom stretch coefficient input means 25, which function is constant fora given cable. The output of analog computer 48 is connected to ahigh-pass filter 54. The output of high-pass filter 54 is supplied todepth correction computer 20.

The output of depth correction computer 20 is supplied to a recorderdrive 49 which converts the electrical output signal from depthcorrection computer 20 to a mechanical rotational output. Thismechanical rotational output is supplied to a junction point 56. Oneoutput from junction point 56 drives chart 50 within recorder 14 viashaft 58. Conductors 15 and 16, which provide the logging measurementsfrom logging tool 10 within the borehole 11, are connected to agalvanometer unit 51 within recorder 14. The mechanical rotationaloutput from junction point 56 via shaft 58 is also connected to a depthindicator 52 within recorder 14. Depth indicator 52 is adapted toprovide depth indications on chart 50 at given intervals of depth, asfor example, each complete rotation of shaft 58. The mechanicalrotational output from recorder drive 49 is also connected through areducing gear 53 to drive wiper arm 27 of potentiometer 28 Within drillpipe correction means 26 and wiper arm 33 of potentiometer 34 withintemperature correction means 32. Thus wiper arms 27 and 33 will rotatein direct relation to the rotational output of recorder drive 49. Shaft59 is also connected to analog computer 48.

Now concerning the operation of the FIG. 1 apparatus, the rotating wheel18 provides mechanical indications to the length measuring device 19 ofthe exact length of cable 12 which passes rotating Wheel 18, and thedirection in which cable 12 is moving, i.e., up or down. Lengthmeasuring device 19 transfers the rotation of rotating wheel 18 intoelectrical impulses indicating the length of cable 12 that is passingrotating wheel 18 and the direction of that travel, to depth correctioncomputer 20. By accumulating these electrical impulses, the totalmeasured cable length Lm could be obtained.

Before discussing the correction by depth correction computer 20 of themeasured length Lm, it is desirable at this time to discuss the equationwhich depth correction computer 20 must solve to provide the correcteddepth. If the distance between the surface of the earth and the centralsurvey electrode of logging tool 10 is considered as the true depth, L0of logging tool 10 in the borehole, it is known that, in most practicalcases, some given length correction ALm must be added to the measuredlength Lln to obtain the true depth L0 of logging tool 10. Thus, can bewritten the equation:

It has been discovered that the relationship for the given additionallength ALm can be represented by the mathematical expression:

ALPE EL(ATu+Td) -ELLATudLjl (fL) where E is the stretch coefiicient;

L is the cable length; v

ATu is the change in tension on the cable measured at th surface of theearth with respect to a known reference tension;

ATd is the change in tension measured by a downhole tension devicelocated between the tool and the bottom end of the cable with respect toa know reference tension;

Lt is the stretch of the cable due to changes in temperature in theborehole;

Leal is the calibrated cable length correction caused by anyinaccurateness of length measuring device 19;

ud is the change in cable length caused by a change in downhole tensionATd as calculated by analog computer `48;

fL is a symbolic operator indicating a low frequency cornponent (a termmultiplied by the operator f1, indicateS that that term includes onlylow frequency components);and

fh is a symbolic operator indicating a high frequency component (a termmultiplied by the operator fh indicates that that term includes onlyhigh frequency components). l Looking now at FIG. there is shown a plotof cable stretch versus borehole depth for a typical run in the borehole11. It can be seen that as the tool is lowered into the borehole 11, thecable stretch continues to increase. When the cable reeling device atthe surface of the earth decreases in speed, there is a sudden change incable stretch, as indicated at point A in FIG. 5. When the cable reelingdevice stops unreeling cable before reversing direction, as indicated atpoint B, there is another substantial change in cable stretch of cable12.

Likewise, when the cable reeling device increases speed when the tool 10is coming out of the borehole 11, as

indicated at point C, there is another sudden change in cable stretch.If there were no changes in speed or direction of the tool 10 travelingin the borehole 11, the measured length indications from rotating wheel18 and length measuring device 19 of FIG. 1 would, after accumulation,indicate substantially accurately the true depth of the tool 10 in theborehole. However, speed changes, reversals of direction, and erratictool motion cannot be sensed by rotating wheel 18 and length measuringdevice 19.

However, it is possible by utilizing an uphole cable tension measurementmade at the surface of the earth to ascertain the average or steadystate values of cable stretch caused by speed changes and reversals indirection. The exact instant of these occurrences cannot be accuratelydetermined because 0f the delay caused by the long length of cable.Also, there are certain assumptions that must be made before a cabletension measurement at the surface of the earth can be accuratelyutilized to correct for cable stretch, which assumptions may beerroneous. It must be assumed that the increase in cable tension changeslinearly with increasing distance from the lower end of the cable, andthe drag forces acting on the cable above its midpoint will be of amagnitude corresponding with the drag forces acting on the cable belowits midpoint.

To provide a more accurate determination of the steady state value ofcable stretch and avoid erroneous assumptions, the apparatus of thepresent invention measures the tension at both ends of the cable 12 andaverages the total. This operation is represented by the 1/2EL(ATu-{ATd)(fL) portion of Equation 2. The total (fr.) portion of Equation 2provides the steady state correction of cable stretch due to tension.

Looking again at FIG. 5, there is shown a point D on the solid linecable stretch portion of FIG. 5. Point D represents the tool 10 becomingmomentarily stuck on the wall of the borehole as it is being raised, andthen becoming unstuck and oscillating before reaching equilibrium. Dueto the long length of cable and the damping coefiicient B of the cable,a surface tension measuring device might not sense this erratic toolmotion, and at best, the tension arriving at the surface of the earththrough the great length of cable, would be vastly distorted. Tocircumvent this potentially substantial type of depth error, the tensionexisting downhole at the tool is measured a the tool and transmittedinstantaneously by distortionless electrical signals to the surface ofthe earth where the depth error caused by this erratic tool motion iscalculated by an analog computer 48 and then then supplied to the totaldepth correction digital computer 20 where it is combined with the otherdepth correction functions. Since the low frequency portion (f1.) ofEquation 2 supplies the steady state depth correction, a high frequencycomponent is added to such portion shown as udQh) in Equation 2, tocorrect for erratic tool motion udUh) is the depth correction fromanalog computer 48 representing the instantaneous depth correctionobtained from the downhole tension measurement.

Referring back to FIG. 1, the downhole tension function ATd is obtainedfrom the downhole tension measuring device 38 located between thelogging tool 10 and the bottom of cable 12. A direct-current (DC) powersupply 40 located at the surface of the earth supplies DC power throughcable conductor 43 to amplifier 41 and oscillator 40 within downholehousing unit 10a. Oscillator 40 supplies a constant voltagealternating-current (AC) signal to bridge circuit 39, the output ofwhich is supplied to amplifier 41. When the tension between tool 10 andcable 12 varies, the resistance of semi-conductor strain gage elementsR2 and R4 varies proportionally to this tension. Looking at bridgecircuit 39, where semi-conductor strain gage elements R2 and R4 arerepresented as dotted line resistors R2 and R4', it can be seen that asthe resistance of R2 and R4' varies, the AC voltage applied from bridgecircuit 39 to amplifier 41 will vary proportionally to this downholetension. Since the resistance R2' and R4 of semi-conductor strain gageelements R2 and R4 are located diagonally opposite each other in bridgecircuit 39, the voltage supplied to amplifier 41 is twice the magnitudeas would be the case with only one semi-conductor strain gage element.

Amplifier 41 supplies an AC signal proportional to the voltage suppliedfrom bridge circuit 39 through DC blocking capacitor 42, which capacitoris adapted to prevent DC power from reaching the output of amplifier 41.This AC tension signal from amplifier 41 is supplied via cable conductor43 to amplifier 45 through capacitor 44, which capacitor is adapted toremove the DC power from the input to amplifier 45. By using capacitors42 and 44 and inductors 43a and 4317, a single conductor 43 can beutilized both to supply DC power to the downhole ten-A sion circuitwithin housing unit 10a and to supply the AC signal proportional todownhole tension to amplifier 45. After amplification by amplifier 45,the downhole tension signal is applied to phase-sensitive detector 46.Another output from amplifier 45 is supplied to voltage-limiting circuit47 whose output provides a phase-reference signal of constant voltage tophase-sensitive detector 46. Phasesensitive detector 46 detects themagnitude of the signal from amplifier 45 which is in-phase with thesignal from voltage-limiting circuit 47 and supplies a resulting DCoutput signal proportional to tension to analog computer 48.

Before a logging operation begins, the tension signal output fromphase-sensitive detector 46 is set at 0 volts by suitable means, as forexample, an initial condition (IC) potentiometer included withinphase-sensitive detector 46. This voltage initial condition is set tocorrespond to a given reference tension from tension device 38, in thiscase, zero tension. Thus, the voltage output from phase-sensitivedetector 46 will represent a change in tension ATd from this referencetension. This downhole tension function ATd is supplied to analogcomputer 48 where the depth error due to downhole tension is computed.

The relationship for the change in tension ATd output fromphase-sensitive detector 46 can be written as:

where u is the depth error due to the change in downhole tension, is thefirst time derivative of the depth error u,

is the second time derivative of the depth error u,

M is the mass of the cable,

B is the damping coeflicient,

E is the stretch coefficient of the cable,

L is the cable length.

Analog computer 48 solves Equation 3 and provides an output signalindicative of the depth error u. Since the E, B and L terms of Equation3 are variable, means are provided to supply these to analog computer48. Analog computer 4S will be explained in greater detail in connectionwith FIG. 4.

Now concerning the surface tension measurement, the apparatus forobtaining this measurement comprises tension device 22 and bridgecircuit 23. The cable 12 is reeled in and out over idler-pulley 17. Anychange in tension on cable 12 is transmitted to idler-pulley 17, whichtension in turn is sensed by surface tension device 22. Surface tensiondevice 22 forms a leg of a resistance bridge circuit within bridgecircuit 23 in the same manner as bridge circuit 39 within downholehousing unit 10a. Bridge circuit 23 includes a power means whichprovides a DC output signal from bridge circuit 39 proportional to thetension on tension device 22. Like the downhole tension output fromphase-sensitive detector 46, the surface tension output from bridgecircuit 23 is set at zero volts when the tension on tension device 22 isat a reference tension, in this case, zero tension.

Now referring to Equation 2, there is a low frequency component L and ahigh frequency component fh thereof. Since the average value of depthcorrection due to tension is only concerned with the low frequencycomponent L, We must filter out the high frequency component ud(fh) ofEquation 2. Thus, at low frequencies representing the average value ofdepth change, the term udUh) is dropped from Equation 2. However, at lowfrequencies, we still have a downhole tension term, 1/zELAtd in Equation2. Therefore, this term must be allowed to pass from analog computer 48to depth correction computer at low frequencies. However, looking atEquation 3 and dropping the high frequency terms and it can be seen thatthe relation for the low Ifrequency component of depth error ud is:

From Equation 2 it is seen that the low frequency component of downholetension is equal to one-half the value represented in Equation 4.Therefore, we must filter the output of analog computer 48 in such amanner that at low frequencies, one-half of the output signal fromanalog computer 48 is applied to depth correction computer 20 and athigh frequencies, the entire output of analog computer 48 is applied todepth correction computer 20. Looking at FIG. 1, there is shown ahigh-pass filter 54 between the output of analog computer 48 and depthcorrection computer 20 which performs this function. The gain versusfrequency characteristics of high-pass filter 54 are shown in FIG. 6M),in a log-log plot. From FIG. 6(a), it can be seen that one-half of theinput voltage is passed at low frequencies, and the total input voltageis passed at high frequencies.

Referring back to Equation 2, it can be seen that the entire upholetension component is utilized at low frequencies only. Thus, the outputfrom uphole tension bridge circuit 23 that is applied to depthcorrection computer 2f) must be at full value at low frequencies andreduced to zero at high frequencies. This function is performed bylow-pass filter 55 which is connected between the output of upholetension bridge circuit 23 and the input of depth correction computer 20.Looking at FIG. 6(b), there is shown the frequency response of low-passfilter 55, in a log-log plot. From FIG. 6(b), it can be seen that thetotal input voltage is blocked at high frequencies. It is seen that thefrequency at which low-pass filter 55 changes the output from surfacetension bridge circuit 23 from full value to zero is the same frequencyat which high-pass filter 54 changes the output of analog computer 48from one-half value to full value. This crossover frequency should berelatively low so that the downhole tension measurement will be fullyeffective over a wide range. A desirable value for this frequency hasbeen found to be 0.1 cycles per second, for example.

Thus, by utilizing the uphole tension function in combination with adownhole tension function, the depth error caused from the total steadystate cable stretch and the cable stretch due to erratic tool motion canboth be accurately corrected. Alternatively, the filters 54 and 55 couldbe deleted by supplying ATu in unfiltered form and designing analogcomputer 48- so that the downhole tension function takes into accountthe depth correction made by the surface tension function ATu.

Looking at Equations 2 and 3, there is shown a term E which representsthe stretch coefficient of the particular cable being utilized. Thisvalue of stretch coefficient is constant for any given cable, but variesfrom cable to cable. The stretch coefficient for a given cable can bemeasured prior to being used in logging runs. Therefore, it is desirableto supply to depth correction computer 20, which solves Equation 2, andanalog computer 48, which solves Equation 3, the correct value of thestretch coefficient E for the particular cable being utilized. Thuslooking at FIG. 1, there is shown a means 25 for supplying the value ofstretch coefficient E to depth correction cornputer 20 and analogcomputer 48.

The length measuring device 19 provides an output pulse at very shortintervals of length, in this case, onequarter of an inch. Even thoughmeasuring device 19 is reasonably accurate in the measurement of thelength of cable 12 being reeled in or out of the borehole 11, a verysmall error present in each one-quarter inch length determination causedby manufacturing tolerances will become unreasonably high when the cable12 is thousands of feet in the borehole 11. Thus -it is desirable tocalibrate length measureing device 19 and correct depth correctioncomputer 20 according to this calibration. This is accomplished bydetermining the exact error involved over many thousands of feet ofcable travel and inserting a calibration correction into depthcorrection computer 20 at certain intervals of length in accordance withthis calibrated correction. This means is shown as calibrationcorrection means 24 in FIG. l, which supplies a function designated Lealto depth correction computer 20.

A depth error can also be caused by high temperatures in the borehole 11which causes an additional stretch of cable 12. The temperature Withinthe borehole 11 varies with the depth of borehole 11. Thus when thelogging tool 10 is at the top of the borehole, there will be little 13or no depth error caused by temperature, and when at the bottom of theborehole 11, the depth error due to temperature will be at a maximum.Thus, a means is required to provide a function to depth correctioncomputer which function increases as the depth of tool 10 withinborehole 11 increases.

To accomplish this, a temperature correction means 32 provides an inputsignal L1 to depth correction computer 20. This signal Lt is derivedfrom the wiper arm 33 of potentiometer 34. The resistance portion ofpotentiometer 34 has a fixed value of resistance from one end ofpotentiometer 3-4 to the other end. However, before a logging run ismade in the borehole, the temperature reading of the borehole isdetermined by suitable means, as for example, running a temperaturetransducer through the borehole. ln practice, however, the temperaturein the borehole is known with suflicient accuracy from prior readingsfrom other boreholes in the area. The readings obtained from thesetemperature measurements can be utilized to adjust variable resistors36, which variable resistors are in parallel with segments of theresistance portion 35 of potentiometer 34 to obtain the desiredtemperature correction curve.

Since this temperature correction varies with the depth of tool 10within the borehole 11, the output of recorder drive 49, as taken fromjunction point 56 is connected through gear 53 to rotate the wiper arm33. The rotation of the output shaft from recorder drive 49 isproportional to the corrected cable length. This mechanical output isconnected through gear 53, which is geared such that the rotation of theoutput shaft from recorder drive 49 can be utilized with potentiometer34. The battery 37 supplies a DC voltage between the end portions of theresistance portion 35 of potentiometer 34, with the negative terminal ofthe battery connected to ground. The wiper arm 33 is at the ground sideof the resistance portion 3S of potentiometer 34 and moves toward thepositive side thereof (counterclockwise in FIG. 1) as the tool 10 islowered into the borehole 11.

Thus, the temperature correction to be applied to depth correctioncomputer 20 will be zero when tool 10 is at the surface `of the earthand will be at a maximum when tool 10 is at the bottom of borehole 11since as the output shaft from recorder drive 49 rotates as the tool 10is lowered into borehole 11, the wiper arm 33 will move in acounterclockwise direction, thus causing the voltage on wiper arm 33 toincrease as the depth of tool 10 Within borehole 11 increases. When thetool 10 is being raised in the borehole 11, wiper arm 33 will rotate inthe opposite direction causing the Voltage on wiper arm 33 t0 decrease.

Looking now at Equation 2, it can be seen that all of the terms thereofare applied to depth correction computer 20 in FIG. 1. Thus, from all ofthe above-described inputs to depth correction computer 20, Equation 1can be solved to obtain the true depth of tool 10 Within borehole 11.However, -in some cases, the true depth is not the depth utilized inperforating an earth strata. adjacent to borehole 11 to obtain the oilpresent therein. In some cases, the depth at which to perforate for oilflow is determined according to the length of drill pipe. This drillpipe length is measured as the drill pipe lays at the surface of theearth without tension in the drill pipe. However, when the drill pipe isin the borehole 11, the tension exerted by the Weight of the drill pipein the borehole along with the temperature in the borehole and otherfactors, causes the drill pipe depth to not coincide with the truedepth.

Thus, it can be seen that a function to correct for this drill pipeerror must be applied to depth correction computer 20, which functionwill be negative since length must be subtracted for drill pipecorrection. This correction is applied by way of drill pipe correctionmeans 26. The wiper arm 27 of potentiometer 28 within drill pipecorrection means 26 provides a signal Ldp to depth correction computer20 to provide this correction. The potentiometer 28 within drill pipecorrection means 26 operates in the same manner as potentiometer 34within temperature correction means 32. The output of recorder drive 49is applied through gear 53 to drive wiper arm 27. The resistance portion29 of potentiometer 28 is a fixed value of resistance. However there areshown variable resistors 30 in parallel across given segments ofresistance portion 29. These variable resistors 30 are adjusted before alogging run according to a drill pipe correction chart obtained from thedriller or if none are available, according to a reasonabledetermination of drill pipe correction. When logging tool 10 is at thesurface of the earth, wiper arm 27 will be at the ground side of theresistance portion 29 of potentiometer 28, thus providing zero volts todepth correction computer 20. As the depth of tool 10 within borehole 11increases, Wiper arm 27 will rotate in a counterclockwise direction,thus increasing the negative voltage applied to depth correctioncomputer 20 from drill pipe correction means 261.

The equation for the output of depth correction computer 20 to recorderdrive 49 representing the corrected depth indication Lc (afteraccumulation of this output) can now be written as:

Where Ldp is the drill pipe correction. Thus, the relationship for thecorrected depth Lc can now be written, combining Equations 1, 2 and 5as:

Equation 6 thus represents the output of depth correction computer 20.The differential version of Equation 6 from computer 20 is applied torecorder drive 49, the mechanical rotational output of which is appliedthrough junction point 56 to gear 53 and to recorder 14 by way of shaft58. Shaft 58 provides the movement for chart 50 and also applies themechanical input to depth indicator 52, which has a mechanism forindicating the depth on chart 50 at given intervals. The loggingreadings from logging tool 10 which are applied by conductors 15 and 16to galvanometer 51 are recorded on chart 50. Thus it can be seen thatthe logging readings applied to chart 50 by galvanometer 51 are referredto the corrected depth as applied by depth indicator `52.

Any one of the above-described correction inputs are cable lengthcharacteristics, which characteristics cause the cable lengthindications from length measuring device 19, after accumulation, to bedifferent from the desired cable length indication. Any one of thecorrection inputs could be utilized to correct for cable lengthindication errors without the other correction inputs. Thus, thecalibration correction or drill pipe characteristi-c could be utilizedwithout the temperature or tension characteristic, etc., but of course,the more characteristics that are used, the more accurate will be thecable length indication, the mos-t accurate being when all of thecharacteristics are used. Thus, when only one characteristic is used,the desired cable length indication will be the combination of Lm andthe function derived from that one characteristic, and so on, with morethan one characteristic.

Referring now to FIG. 4, there is shown the analog computer circuit 48.The output of phase-sensitive detector 46 of FIG. 1 is connected to axed resistor R11, the other side of which is connected to a point X. Thepoint X is connected to a high input impedance amplifier A1, whoseoutput is connected to one side of the resistance portion of apotentiometer R14, the other side of the resistance portion ofpotentiometer R14 being connected to ground. The wiper arm ofpotentiometer R11 is connected through a fixed resistor R13 back to thepoint X. The output of amplifier A1 is also connected through a fixedresistor R6 to a point Y. The point Y is connected to a high inputimpedance amplifier A2. The output of amplifier A2 is connected to oneside of the resistance portion of a potentiometer R7, the other side ofthe resistance portion of R7 being connected to ground. The wiper arm ofpotentiometer R7 is connected through a fixed resistor R back to thepoint Y. The output of amplifier A2 is also connected through acapacitor C1 back to the point Y.

The output of amplifier A2 is also connected through a fixed resistor R8to a point Z. The point Z is connected to the input of a high inputimpedance amplifier A2, the output of which is connected through avoltage dividing network comprising resistor R9 andR10 to ground. Thejunction point between resistors R9 and R10 is connected to a first side60 of the resistance portion of a potentiometer R12, the other side ofthe resistance portion of potentiometer R12 being connected to the pointX. The -first side 60 of potentiometer R12 is also connected to a firstwiper arm 68 of potentiometer R12. The other side 61 of the resistanceportion of potentiometer R12 is also connected to a second wiper arm 69of potentiometer R12. The output of amplifier A3 is also connectedthrough a capacitor C2 back to the point Z. The output of arnplifier A3is also connected to the high-pass filter 54 of FIG. 1. The wiper arm ofpotentiometer R14 and the first wiper arm 68 of potentiometer R12 arerotated by the shaft 59 from gear S3 of FIG. 1. Thus, the wiper arm ofpotentiometer R14 and the first wiper arm 68 of potentiometer R12 rotateacross the resistance portion of potentiometers R12 and R14 with therotation of shaft 59.

Now concerning the operations of the analog computer circuit 48 of FIG.4, analog computer 48 is adapted to solve Equation 3 and provide anoutput signal indicative of the depth error ud. To solve Equation 3, asignal indicative of the second derivative tid of the depth error u'dmust be applied to a series of integrating circuits. Therefore, thesecond derivative tid of depth error ud must be solved from Equation 3,

The signal at the input to amplifier A2 (point Y) will be considered asthe second derivative 'd of the depth error ud. Thus the signal at theoutput of amplifier A2 will be the first derivative tid of the deptherror wd, and the signal at the output of amplifier A3 will be equal tothe depth error ud. The voltage at the junction point between resistorsR9 and R10 will be equal to kud where Rio RVi-Rio Thus, the ud portionof Equation 7 is multiplied by this constant, k. If now that portion ofpotentiometer R12 between point 60 and wiper arm 68 and that portion ofpotentiometer R14 between ground and the wiper arm are set equal to a,and the total value of the resistance portion of potentiometer R12 isset equal to the stretch coefficient E of cable 12 by adjusting wiperarm 69 of potentiometer R12, can be written the relationship RJ11-M canbe written. Thus, can be set proportional to the damping coefficient B.Therefore before logging a given borehole with a given cable, the valueof the stretch coefficient of the Gebl@ E and the value of the dampingand coefficient B, can both be set by wiper arm 69 of potentiometer R12and the wiper arm of potentiometer R7 respectively.

Since the length of cable within the borehole 11 varies as the tool 10is raised and lowered in the borehole 11, wiper arm 68 of potentiometerR12 and the wiper arm of potentiometer R14 are connected to shaft 59from gear 53 so that the length term L can be continuously supplied tothe analog computer 48. Thus, it can be seen that analog computer 48solves Equation 3 and supplies a signal to high-pass filter 54indicative of the depth error ud.

Referring now to FIG. 2, portions of the FIG. 1 apparatus are shown ingreater detail, which portions comprise the depth correction computer20, length measuring device 19, and recorder drive 49. Referring firstto length measuring device 19, there is shown the cable 12 in contactwith the rotating wheel 18 in such a manner that when the cable 12 movesup or down, rotating wheel 18 will rotate with this movement of cable12. Rotating wheel 18 is mechanically coupled to rotating drum 70 suchthat rotating drum 70 will rotateV as the rotating wheel 18 turns.Located within rotating drum 70 and on the axis thereof is a lightsource 71. Located on the cylindrical surface of rotating drum 70 are aplurality of slits, only a few of which are shown. The illustrated slitsare designated 72, 73, 74 and 75. All of the slits on the cylindricalsurface of rotating drum 70 are divided into three tracks. Slit 72 and73 on the extreme left are part of a first track A, slit 75 on theextreme right side of rotating drum 70 is part of a second track C, andslit 74 located intermediate of tracks A and C is part of a third trackB. These slits extend around the total circumference of rotating drum70.

Located a fixed distance from the cylindrical surface of rotating drum70 is a sensing device 76 having three photocells thereon designated A,B and C. The photocells A, B and C are positioned with respect to tracksA, B and C on rotating drum 70 such that photocell A will only sense thelight from light source 71 coming through those slits on track A,photocell B will only sense the light coming through those slits ontrack B, and photocell C will only sense the light coming through thoseslits on track C.

Looking now on the left hand side of FIG. 2 below length measuringdevice 19, there are shown the means for supplying the input functionsto depth correction computer 20. These input means are the same as thoseshown in FIG. l and have the same reference numbers as in the FIG. 1apparatus. These input means comprise calibration correction 24 whichsupplies an input signal to a calibration logic circuit 76 withincomputer 20, drill pipe correction means 26 which supplies an inputsignal to adding-network 77 within computer 20, and temperaturecorrection means 32 which also supplies an input signal toadding-network 77. These input means further comprise downhole tensionanalog computer 48 which supplies a signal to high-pass filter 54, theoutput of which is supplied to adding-network 77, and such tensionbridge circuit 23 which supplies an input signal to low-pass filter 55,whose output is supplied to the resistance portion of a potentiometer78. The wiper arm of potentiometer 78 is controlled by a mechanicaloutput from stretch coefficient input means 25, which could comprise,for example, a manually operated shaft 112 adapted to rotate the wiperarm of potentiometer 78.

The opposite side of the resistance portion of potentiometer 78 and thewiper arm thereof are connected to one side of the resistance portion ofthe potentiometer 89, the other side of the resistance portion thereofconnected to ground. The wiper arm of potentiometer 89 is connected toan input of adding-network 77. Adding-network 77 is adapted to isolatethe inputs supplied thereto from each other, while at the same timeadding the respective signal inputs and applying one output signal to aninput of differential amplifier 90. The output of differential amplifier90 is supplied to Schmitt triggers 91 and 92. The output from Schmitttrigger 91 is connected to the input of a bi-directional counter 93 ofstandard design and to an input of a logic circuit 94. The output ofSchmitt trigger 92 is connected to an input of bi-directional counter 93and an input of a logic circuit 95. Logic circuits 94 and 95 are shownin greater detail in FIG. 3. The output of bi-directional counter 93 isconnected to the input of a digital-to-analog converter 96 of standarddesign, whose output is connected back to a second input of differentialamplifier 90.

The output of low-pass filter 55 is also connected to the resistanceportion of a potentiometer 88, the other side thereof being connected toground. The wiper arm of potentiometer 88 is connected to an input of ananalogto-digital converter with a serial output 97 of standard design.Also supplied to analog-to-digital converter 97 is the command todigitize output signal from counting circuit 87. The output fromanalog-to-digital converter 97 is supplied to a binary counter 98 ofstandard design. When the accumulated count of binary counter 98 reachesa predetermined number, a flip-flop 187 is set so as to apply a 1 to theinhibit portion of the pulse sample and gate circuit 80 and reset thebinary counter 98. The flip-flop 187 is then reset by the control signalG from the circuit 80.

The output from direction sensor 83 is supplied to inputs of logiccircuits 94 and 95 and inputs of translators 86 and 108. The down outputfrom logic circuit 9S and the up output from logic circuit 94 areconnected to the inhibit portion of pulse sample and gate circuit 80.The up output from logic circuit 95 and the down output from logiccircuit 94 are connected to the add portion of pulse sample and gatecircuit 80.

Photocells A, B and C of sensing means 76 supply outputs to trigger andlogic circuit 79. Trigger and logic circuit 79 supplies inputs to pulsesample and gate circuit 80, delay logic circuit 81, binary counter 113,and direction sensor 83. The output from binary counter 113 is suppliedto an input of calibration logic circuit 76. Delay logic circuit 81supplies an input to corrector 82. The output from corrector 82 issupplied to the input of a iiip-iiop 84 and one input of an inhibit gate115, whose output is supplied to recorder drive 49 outside of depthcorrection computer 20. The control input to inhibit gate 115 issupplied from an output of pulse sample and gate circuit 80. The outputfrom flip-flop 84 is connected to the input of a flip-flop 85, whoseoutput is connected to a translator 86 of suitable design, as forexample, the Slosyn Translator manufactured by Superior ElectricCompany. Translator 86 comprises a series of switching circuits fortranslating the serial pulses from depth correction computer 20 to aparallel form suitable for driving stepmotor 109. The output offlip-flop 85 is also connected to counting circuit 87 of standarddesign, comprising a series of flip-flops. Counting circuit 87 providesa command to digitize output signal every one foot of cable travel.Trigger and logic circuit 79, delay logic circuit 81, corrector 82,calibration logic 76, pulse sample and gate circuit 80, and directionsensor 83 are shown in greater detail in FIG. 3.

Calibration logic circuit 76 supplies outputs to both the inhibitportion and add portions of pulse sample and gate circuit 80. Pulsesample vand gate circuit 80 provides an output to delay logic circuit81, a sample output to calibration logic circuit 76, and reset outputsto binary counter 113, binary counter 98 (designated G), andbi-directional counter 93 (designated F). The output from the inhibitportion of pulse sample and gate circuit 80 is supplied to the inhibitfunction of corrector 82 and the output from the add portion of pulsesample and gate circuit 80 is supplied to the add function of corrector82. Also supplied to the add portion of corrector 82 is the output fromthe zero speed portion of pulse sample and gate circuit 80.

The output from translator 86 is supplied to the input of a stepmotor105. The mechanical output from stepmotor is connected throughmechanical counter 106, which counts the revolution of the output shaftlfrom stepmotor 105, to gear 107. The mechanical output from gear 107,shown as shaft 111, rotates the wiper arm of potentiometer 89. Gear 107adapts the rotation of the output Ashaft from stepmotor 105 to therotation of the wiper arm of potentiometer 89.

The output from corrector 82 is connected to a translator 108 withinrecorder drive 49 via the inhibit gate 115. The electrical output fromtranslator 108 is supplied to the input of stepmotor 109, whosemechanical output is connected through gear 110 to recorder 14 ofFIG. 1. The translator 108 which drives stepmotor 109 within recorderdrive 49 is similar in construction to translator 86 which drivesstepmotor 105 within depth correction computer 20. Stepmotor 109 ofrecorder drive 49 must provide more torque to recorder 14 than stepmotor105 must supply to the wiper arm of potentiometer 89, and thus stepmotor109 is larger than stepmotor105.

Now concerning the operation of the apparatus shown in FIG. 2, theoutput pulses from photocells A, B and C of sensing device 76 aresupplied to trigger and logic circuit 79, which squares olf the pulsesfromsensing device 76 by suitable means, as for example, avotlagelimiting circuit or Schmitt trigger, and sends these pulses topulse sample and gate circuit 80 and delay logic circuit 81 at intervalsof one-quarter inch of cable travel. Trigger and logic circuit 79 alsosupplies pulses to direction sensor 83, which determines the directionof travel of cable 12.

The purpose of corrector 82 is to apply a correction to the pulses fromtrigger and logic circuit 79, which pulses represent increments themeasured length Lm of cable 12. Corrector 82 will either inhibit a pulseor add a pul'se to the train of one-quarter inch interval pulsesoriginating from trigger and logic circuit 79. Thus, looking at Equation6, the output from trigger and logic circuit 79 is a differential Ln1portion of Equation 6 and the function applied to corrector 82represents a differential version of the remainder of Equation 6. Eachone-quarter inch interval pulse from trigger and logic circuit 79, whichis supplied to pulse sample and gate circuit 80, originates a series ofsample signals within pulse sample and gate circuit 80 (which will bediscussed in greater detail later).

Delay logic circuit 81 delays the pulse from trigger and logic circuit79 for a suficient time as to allow the correction to be made. If apulse is to be added to corrector 82, the pulse from trigger and logiccircuit 79 must be delayed beyond the time that a pulse is added tocorrector 82.

In addition, pulse sample and gate circuit 80 determines the speed ofmovement of cable 12 past rotating wheel 18 and switches between twodelay circuits within delay logic circuitl 81 depending on the speed atwhich cable 12 is moving, since this speed determines the rate ofonequarter inch interval pulses. Thus, yit can be seen that trigger andlogic circuit 79 supplies a pulse at every onequarter inch interval ofcable travel past rotating wheel.

18, which pulse is delayed by delay logic circuit 81 for the amount oftime required to sample and correct the various correction functions,which correction is supplied to corrector 82. This delay is determinedby the maximum stepping rate of the stepmotor 109 in the recorder drive49.

Corrector 82 supplies the corrected length Lc pulses to recorder 49 and'ip-liop 84, each pulse still representing one-quarter inch of cabletravel. These one-quarter inch interval pulses from corrector 82 areapplied to recorder drive 49 through inhibit gate 115 to drive recorder14. Thus, each pulse received from corrector 82 is caused to drivestepmotor 109, which drives chart 50 (FIG. 1) of 19 recorder 14 by therequired amount, and therefore recorder 14 comprises a mechanicalstorage for the corrected length LC pulse output from corrector 82.

Now, taking an example of this operation, if in a given interval oftime, the cable 12 opposite rotating Iwheel 18 at the surface of theearth has moved a total distance of l inches, there will be a total of40 pulses supplied from trigger and logic circuit 79 through delay logiccircuit 81 to corrector 82. But, if in actuality, the tool within theborehole has only moved 9 inches, corrector 82 will inhibit 4 pulsesfrom trigger and logic circuit 79 within this interval of time. Thus thetotal output within this interval of time will be a total of 36 pulses,which 36 pulses after being transferred to a mechanical rotation byrecorder drive 49, will be stored in recorder 14 in the form of theposition of chart 50 of recorder 14 (see FIG. 1) as a total of 9 inchesof tool travel. If the actual change in length had been ll inches on theother hand, corrector 82 would have added 4 pulses and thus recorder 14would indicate an l1 inch change.

Now concerning the input to be supplied to corrector 82, the purpose ofdepth correction computer 20 is to solve Equation 6 and supply theresult to recorder drive 49. The calibration correction function issupplied from calibration correction means 24 to calibration logiccircuit 76. Looking at IEquation 6 and FIG. 2, thecalibration correctionLm from calibration correction means 24, drill pipe correction Ldp fromdrill pipe correction means 26, and temperature correction Lt fromtemperature correction means 32, are all supplied directly toadding-network 77 within computer 20, which acts to isolate the inputswhile, at the same time, adding the inputs to provide one output todifferential amplifier 90. The downhole tension depth error functionud(fh) and 1/2ELATdffL) terms of Equation 6 are supplied from high-passfilter 54 to adding-network 77 to be added to the other inputs thereto.The uphole tension bridge circuit 23 supplies the ATu term whichlow-pass filter 55 reduces to zero at high frequencies.

However, there still remains the input of the stretch coefficient E termand the length L term of Equation 6. The length L term is obtained fromthe corrector 82 output of depth correction computer 20 and is suppliedby the output shaft 111 from gear 107 to the wiper arm of potentiometer89. The one-quarter inch interval pulses from corrector 82 becomeone-half inch interval pulses on the output of fiip-fiop 84 and one inchinterval pulses on the output of flip-flop 85. These one inch intervalserial pulses are translated by translator 86 into parallel form todrive stepmotor 105. The direction of cable travel is supplied totranslator 86 from direction sensor 83. The mechanical rotational outputfrom stepmotor 105 rotates the wiper arm of potentiometer 89 by shaft111. Thus, the position of the wiper arm of potentiometer 89 on theresistance portion of potentiometer 89 is indicative of the correctedlength Lc of the tool in the borehole. When the wiper arm ofpotentiometer 89 is at the ground point of the resistance portion ofpotentiometer 89, it is seen that the voltage input to adding-network 77from filter 55 is zero, thus indicating zero cable length. By the sametoken, when the wiper arm is at the top of the resistance portion ofpotentiometer 89, there is a maximum voltage applied to adding-network77 and thus the cable length is at a maximum.

Now referring to the stretch coefficient E input to depth correctioncomputer 20, since the stretch coeicient E varies for different cablesbut is the same for any given cable, the value of the stretchcoefiicient E can be inserted into depth correction computer 20 before alogging run and remain at that value. To accomplish this, the stretchcoefficient input means 25 is mechanically coupled to the wiper arm ofpotentiometer 78 and the wiper arm of potentiometer 88. The position ofthe wiper arm of potentiometer 88 is indicative of the stretchcoefficient E and the position of the wiper arm of potentiometer 78gives the value of E/2. Thus, the signal present on the wiper arm ofpotentiometer 78 is proportional to 1/zEATw the signal present on thewiper arm of potentiometer 89 is proportional to lzELATu, and the signalpresent on the Wiper arm of potentiometer 88 is proportional to EATu.The output from adding-network 77 is thus proportional to therelationship Differential amplifier 90 senses the difference in voltagebetween the output voltage from adding-network 77 and the output voltagefrom digital-to-analog converter 96 and supplies an output voltageproportional to the difference between these applied input voltages. Ifthe applied input voltage from adding-network 77 is greater than theapplied input voltage from digital-to-analog converter 96 by aprescribed amount, Schmitt trigger 91 is energized and provides anoutput signal to the plus input terminal of bi-directional counter 93.When the correction is made by corrector 82, a pulse is sent tobi-directional counter 93 from pulse sample and gate circuit on output Fto cause bi-directional counter 93 to count forward. Digitalto-analogconverter 96 converts the count present in bidirectional counter 93 toan analog signal which is supplied back to differential amplifier thuscausing the output of differential amplifier 90 to return to 0 volts, ifonly one count has been accumulated. This resets Schmitt trigger 91, ifdifferential amplifier 90 is returned to zero, to enable Schmitt trigger91 to be ready for another input.

By the same token, if the input to differential amplifier 90 fromadding-network 77 should decrease by a prescribed amount, differentialamplifier 90 will have a negative output, thus causing Schmitt trigger92 to switch on. Schmitt trigger 92 then supplies an output signal tothe negative terminal of bi-directional counter 93, causingbidirectional counter 93 to count in a reverse direction via the outputF from corrector 80. The total count within bidirectional counter 93would thus be less, causing the analog output from digital-to-analogconverter 96 which is supplied back to differential amplifier 90 to beless. Thus, the output from differential amplifier 90 will return tozero volts, if only one count is necessary, resetting Schmitt trigger 92for another output from differential amplifier 90. Thus, it can be seenthat differential amplifier 90 supplies an output voltage indicative ofthe magnitude and polarity of the difference between the output voltagefrom adding-network 77 and the accumulated count in bi-directionalcounter 93. Schmitt triggers 91 and 92 monitor the magnitude andpolarity of this difference signal and operate to either add or subtracta Lm pulse in corrector 82 if the magnitude of this difference signalexceeds the threshold level of either trigger 91 or 92. The thresholdvoltage of triggers 91 and 92 are set equal to one-quarter inch of cablestretch.

If now a very large voltage is supplied from addingnetwork 77 todifferential amplifier 90, Schmitt triggers 91 and 92 can only provideone output pulse at a time since their threshold voltages are set foronly one-quarter inch of cable travel and bi-directional counter 93 mustbe reset by the output F from pulse sample and gate circuit 80` beforeanother count can be registered. The output voltage from Schmitttriggers 91 or 92 applied to bi-directional counter 93,digital-to-analog converter 96, and subsequently back to differentialamplifier 90 in the form of an analog signal, will still leave a largevoltage output from differential amplifier 90 since only that portion ofvoltage due to one-quarter inch of cable stretch has been taken awayfrom the output of differential amplifier 90. Thus, one of Schmitttriggers 91 or 92 will remain energized, providing another count tobi-directional counter 93, thus reducing the difference between theinputs to differential amplifier 90 still more. This process continuesuntil the two inputs to differential amplifier 90 are within aprescribed voltage difference of one another.

Since the output pulses from Schmitt triggers 91 and 92 each representone-quarter inch of cable stretch, these output pulses from Schmitttriggers 91 and 92 are utilized 1n the correction of the measured lengthLm pulses from delay logic circuit 81. The output pulses from Schmitttriggers 91 and 92 are supplied to logic blocks 94 and 95 respectively,which logic blocks determine whether a pulse should be added to orinhibited from the measured length Lm pulses depending on whether thelogging tool is moving up or down the borehole. If the tool 10 is movingdown the borehole, each L,rn pulse represents an increase in depth ofthe tool within the borehole. Therefore if the cable 12 stretches, apulse must be added to the length measurement Lm, and if the cabledecreases in stretch, a pulse must be inhibited from the output of delaylogic circuit 81. On the other hand if the tool is moving up theborehole, each pulse represents a decrease in depth of tool 10 withinthe borehole. Therefore in this case, if the cable 12 stretches, a pulsemust beinhibited rfrom reaching recorder drive 49 and on the other handif the cable 12 decreases in stretch, an additional pulse must be addedto recorder drive 49.

Logic circuits 94 and 95 accomplish this function. Direction sensor 83supplies a signal to logic circuits 94 and 95 indicating the directionof travel of cable 12. This input signal from direction sensor 83switches between the up and down outputs of logic circuits 94 and 95.That is, when the vcable 12 is moving down, the down outputs of logiccircuits 94 and 95 are enabled to be energized and when the cable 12 ismoving up, the up outputs are enabled to be energized. The down outputfrom logic circuit 95 and the up output from logic circuit 94 aresupplied to the inhibit function of corrector 82 by way of the inhibitportion of pulse sample and gate circuit 80. The up output from logiccircuit 95 and the down output from logic circuit 94 are supplied to theadd function of corrector 82 by Way of the add portion of pulse sampleand gate circuit 80.

Thus it can be seen that when cable 12 is moving in a downwarddirection, a cable stretch pulse from Schmitt trigger 91 will besupplied to the add function of corrector 82 and a reduction in cablestretch from Schmitt trigger 92 will be applied to the inhibit functionof corrector 82. On the other hand when the cable is moving up theborehole, a cable stretch output from Schmitt trigger 91 will be appliedto the inhibit function of corrector 82 and a reduction in stretchoutput from Schmitt trigger 92 will be applied to the add function ofcorrector 82. After the add or inhibit function is applied to corrector82, pulse sample and gate circut 80 supplies a pulse to bi-directionalcounter 93 (output F) to cause bi-directional counter 93 to countforward or backward, depending on whether the or input of counter 93 isenergized.

Now concerning the calibration correction input to corrector 82 of depthcorrection computer 20, this calibration correction concerns thecalibration of length measuring device 19 and rotating wheel 18 attachedthereto. Even though the maximum error that could be present on each ofthe one-quarter inch pulses from trigger and logic circuit 79 isextremely small, the aggregation of an extremely small error over anextremely long distance, such as the distance to the bottom of theborehole, may be substantial. Thus the rotating wheel 18 and lengthmeasuring device 19 are calibrated before being utilized in a loggingrun. The resulting calibration correction is set into the calibrationcorrection means 24. Binary counter 113 counts the number of one-quarterinch pulses from trigger and logic circuit 79. Calibration correctionmeans 24 provides the information to calibration logic circuit 76concerning the count that binary counter 113 should reach before acorrection is applied to corrector 82. Calibration logic circuit 76comprises a series of AND gates in a conventional manner, or one ANDgate connected to various 22 ones of the stages of binary counter 113,which stages depending on the desired count of binary counter 113.Calibration correction means 24 also supplies the information as towhether a pulse should be inhibited or added. The outputs fromcalibration logic circuit 76 are supplied to the inhibit and addfunction of corrector 82 through the inhibit and add portions of pulsesample and gate circuit 80. After a calibration correction is suppliedto the corrector 82, binary counter 113 is reset back to zero by pulsesample and gate circuit 80. Thus, it can be seen that at given intervalsof length, a calibration correction pulse is either added to orinhibited from recorder drive 49.

Now concerning the L -EL nTudmfL) term of Equation 6, the circuitry forapplying this correction to corrector 82 comprises analog-to-digitalconverter 97, binary counter 98 to pulse sample and gate circuit 80, andcounting circuit 87 to analog-to-digital converter 97. The input signalfrom the wiper arm of potentiometer 88 which is applied toanalog-to-digital converter 97, is equal to EATu. Analog-to-digitalconverter 97 converts this applied analog voltage into a series ofdigital pulses which are applied to binary counter 98 at given intervalsof length. The on-time of analog-to-digital converter 97 is proportionalto the applied analog voltage, and the frequency is fixed. The giveninterval of length is obtained from the circuitry comprising flip-flops84 and 85 and counting circuit 87. The one-inch interval output pulsesfrom flip-Hop 85 are applied to counting circuit 87, which counts to adesired length, as for example one foot, and applies a command todigitize signal to analog-to-digital converter 97, which causesanalog-to-digital converter 97 to provide the series of digital pulses.The total number of digital pulses is proportional to the applied analogvoltage, during each command to digitize.

Binary counter 98 counts these pulses from analog-todigital converter 97and provides an output pulse to the input of a flip-op 187, the outputof which is supplied to the inhibit portion of pulse sample and gatecircuit This output pulse from binary counter 98 is generated after apredetermined number of pulses has been counted, this predeterminednumber of pulses being equal to onequarter inch of cable stretch, Theoutput of ip-op 187 is also supplied back to the reset input of binarycounter 98, so that binary counter 98 will be reset each time a pulse isgenerated from binary counter 98. Pulse sample and gate circuit 80supplies a signal back to the reset inlput of flip-flop 187 to resetip-tlop 187 for the next output pulse from binary counter 98. This resetsignal is designated G. It can be seen that by this means, binarycounter 98 only stores one-quarter inch of cable travel therein, and theremainder of the L EL ATudLUL) term of Equation 6 is stored in recorder14 in the form of the position of chart 50. Therefore, if power shouldbe lost at any time a maximum of one-quarter inch of cable stretch wouldbe lost.

Now, concerning the time sequence of the various depth correctionoperations, it can be seen that there are three sets of correctioninputs which may be applied to corrector 82. These correction inputs atthe same time are the calibration correction from calibration logiccircuit 76, the

L EL ATudLtfL) term of Equation 6 from binary counter 98, and the outputfrom logic circuits 94 and 95. If there should be a correction on two orthree of these correction inputs, it might seem that all but onecorrection input would be lost since only one input can be applied tocorrector 82 at any given time. To solve this problem each of the

